This invention relates to a method of determining the location in the earth of sub-surface boundaries and/or the acoustic properties of sub-surface features in the earth and to apparatus for this purpose.
A method and apparatus for this purpose are described in British patent application No. 79 13997 in the name of A. M. Ziolkowski and Seismograph Service (England) Limited which formed the basis for British patent application No. 8,013,438, filed on Apr. 23, 1980, now published as British published patent application No. 204841A which comprises employing one or more first and second point sound sources to produce first and second sound waves containing energies of elastic radiation which differ from each other by a known factor, detecting reflections of said first and second waves to generate first and second seismic signals and subjecting said seismic signals to analysis and comparison.
Whilst the method and apparatus there described do have practical application, this is somewhat limited in that they are applicable only to point sources whose far field radiation has spherical symmetry.
It is very often preferable to employ one or more arrays of sound sources, particularly in a marine environment and such arrays generate radiation which is not spherically symmetric; that is the amplitude and phase of a given frequency of the far field radiation are normally dependent on azimuth.
A distributed array of point sources is used for increasing the power of the source, for shaping the far field wavelet, and for improving the directivity of the radiation. If the distance between individual point sources within such an array is less than about a wavelength, the interaction effects between these individual sources are significant. For most point sources these interaction effects are not well understood, and the far field wavelet of an array of such point sources cannot be calculated from a knowledge of the individual far field source wavelets. It must be measured in the far field. Since this measurement is very often awkward or impossible to make, the far field wavelet of such an array is very often unknown.
Air gun arrays are typical in this respect. Although air guns have many practical advantages, the main disadvantage of an air gun as a sound source is the waveform itself. It lacks power, it has a multi-peaked spectrum and, in the time domain, it is inconveniently long and oscillatory; moreover, it is not minimum-phase. Arrays of air guns are often used in an attempt to overcome all these difficulties simultaneously. Some are more easily overcome than others.
The lack of power and lack of bandwidth are remedied simply by using more guns and by using guns of different sizes. The really intractable problem is the phase spectrum of the far field wavelet. If it were minimum phase a least-squares time-domain inverse deconvolution method could be used to remove the wavelet from the data (provided the earth impulse response were white and stationary). But the standard method of deconvolution does not work, because the wavelet is not minimum phase. It has therefore become essential to design an array to produce a wavelet which is so short that it does not need to be deconvolved from the data.
In recent years air gun array design has concentrated on this shortness aspect of the wavelet, while simultaneously attempting to maintain power and bandwidth. This is difficult to do, for shortness can often be achieved only at the expense of losing some energy in the tail of the wavelet.
There is an important measure of shortness known as "primary-to-bubble" or "front-to-back" ratio. This is usually calculated from broadband measurements of far field wavelets. The shortness ratio decreases as the high cut filter is reduced to simulate earth filtering. In other words, the higher frequency energy is concentrated in the front of the wavelet; as this is removed by earth filtering the amplitude of the front of the wavelet decreases faster than the amplitude of the tail and the wavelet appears to get longer. Therefore deconvolution is still required.
It has been noted that even when the wavelet is short it is not minimum phase. In order to remove it from the seismogram its shape must be known and must, therefore, be measured in the far field. Since the shape of the wavelet tends to change during continuous operation, a continuous monitor of the far field wavelet is necessary to effect an adequate deconvolution. If the water is deep it is possible to tow a hydrophone in the far field below the air gun array and to measure the far field wavelet before reflections from the sea floor arrive.
When the water is shallow, it is not possible to measure this wavelet, and since its shape cannot be calculated, there are only three courses open:
1. to use a deep water measurement and then to hope that the wavelet generated in shallow water does not vary too much from from this measurement; PA1 2. to assume that the shallow water wavelet is minimum-phase (knowing all the time that this is extremely unlikely) and to hope that the standard deconvolution method will work; PA1 3. to forget all about deconvolution.